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치의학석사학위논문

Influence of implant number and various

prosthodontic designs on biomechanical

behaviors of the implant-supported fixed

denture in posterior mandible:

A 3D finite element study

하악 구치부에서 임플란트 개수와 다양한

보철디자인이 임플란트-지지고정성보철물의

생역학적 거동에 미치는 영향:

삼차원 유한요소연구

2018 년 8 월

서울대학교 대학원

치의과학과 치과보철과 전공

정 원 경

ABSTRACT

Influence of implant number and various

prosthodontic designs on biomechanical

behaviors of the implant-supported fixed

denture in posterior mandible:

A 3D finite element study

Won Kyung Jung, BDS

Department of Prosthodontics

The Graduate School

Seoul National University

(Directed by professor Ho Beom Kwon, DDS, MS, PhD)

1. Purpose

The purpose of this study was to evaluate the biomechanical

behaviors of implant-supported fixed prostheses with various designs

and different number of implants at mandibular posterior region using

3D finite element analysis.

2. Material and methods

Finite element models consisting of partially edentulous mandible at

posterior region, remaining teeth, implant system (Osstem US system;

Osstem Implant Co.) and prostheses were created based on the

patient’s computed tomographic data. Four models with the variations

were constructed as follows: four implants from first premolar to

second molar with non-splinted crowns (NS); four implants with

splinted crowns (SP); three implants at first and second premolar and

second molar with pontic (PT); two implants at first premolar and

first molar with cantilever design (CT). The frictional coefficient of

0.3 was set among the interfaces of implant system with 825 N of

preload at the implant screw. An oblique force of total 300 N at an

11.3-degree angle to the long axis of the implant was applied to the

occlusal surfaces of the crowns. The von Mises stress and

displacement of each component in the models were evaluated.

3. Results

The results showed that the von Mises stress in implant significantly

increased as the number of implants used in the models were

decreased, mainly for the cantilever design (577.7 MPa in model NS,

616.8 MPa in model SP, 649.3 MPa in model PT and 791.6 MPa in

model CT). On the contrary, cantilever model showed less stress than

other models in cortical bone and crowns (112.2 and 220 MPa

respectively). A non-splinted model resulted in less stress than

splinted one in the components such as cortical bone and implant

(151 and 577.7 MPa in model NS, 182.3 and 616.8 MPa in model SP)

However, lower stresses were observed in cancellous bone and

crowns for splinted model (31.9 and 297.7 MPa in model SP, 36.8 and

298.4 in model NS).

4. Conclusion

The reduction of the number of implants suggested higher stress

concentration in certain components of implant-supported fixed

prostheses. However, there was no significant relation between the

stress concentration and the number of implants in other components

such as bone or crowns. Thus, applying pontic or cantilever designs

could be also acceptable as treatment planning options.

………………………………………………………………………………

Keywords : Implant-supported fixed prostheses, Biomechaniacal

behaviors, Stress concentration, Finite element analysis

Student Number : 2016-22041

CONTENTS

Ⅰ. INTRODUCTION …………………………………… 1

Ⅱ. MATERIAL AND METHODS …………………… 4

Ⅲ. RESULT ……………………………………………… 5

Ⅳ. DISCUSSION ………………………………………… 7

Ⅴ. CONCLUSION ……………………………………… 10

REFERENCES ……………………………………… 11

TABLES ……………………………………………… 16

FIGURES ……………………………………………… 20

국문초록 ……………………………………………… 24

1

Ⅰ. Introduction

Recent clinical researches have showed high success of the

implant-supported fixed prostheses increasing the quality of life of

partially edentulous patients.1-3 However, some implant failures which

caused by various factors have been also reported.4,5 One of them is

the biomechanical factor such as stress distribution, quality of bone,

number of implants, design and location of implants that may affect

the longevity of implants and lead to the success of implant

treatment.6 To reduce the stress distribution to implants and bone

tissue and increase the success rate of implants, favorable treatment

designs should be planned.7

There exist different treatment planning options of implant-supported

partial fixed prostheses using pontics or cantilevers as an alternative

to replace long span of missing teeth. Especially when the posterior

teeth are missing, treatment options with implant-supported fixed

prostheses would be different to those of anterior areas because of

differences in biomechanics with altered anatomy.8 Jivraj et al8

suggested that the outcome of implants in posterior quadrants can be

predicted depending on many variables such as implant position and

number, type of prosthesis and occlusal considerations. Particularly

the choice of the position and number of implants used for multiple

missing teeth may be related to biomechanical factors of implants

how stress is distributed to implant and the surrounding bone.9 Lee

et al10 mentioned that when the number of implant is decreased, the

biomechanical stress in the implant system would increase and it may

cause the bone loss due to its overload. They described that this

outcome may also be associated with bone quality and quantity.10

Moreover, previous studies reported that the type of cantilever

prostheses caused excessive stress concentration in supporting bone

inducing bone resorption and it would affect the longevity of

2

implant-supported fixed prostheses increasing the number of

complications.11-14

Although placing one implant for each missing posterior tooth is one

of common approaches to reduce biomechanical complications, it

would be still controversial how many implants need to be replaced

to rehabilitate the partially edentulous patients due to lack of

scientific evidence and backgrounds especially in biomechanical

concepts for dental practitioners.15,16 To place an implant for each

missing tooth requires thorough consideration with a variety of

clinical situations such as severe bone resorption or cost limitation.8

When even using ideal number of implants is allowed, it also needs

to be considered whether to splint or separate the restorations. It is

common to splint the crown in clinical practice as it distributes the

force applied to the implants minimizing transfer of stress to the

restorations.17-19 However, there are several studies with conflicting

results for splinting crowns as well.20,21 The results in clinical study

of Vigolo et al21 indicated that the implants with non-splinted

restorations could be successfully used for implant treatment showing

overall survival rates compared to those with splinted restorations.

Thus, it is important for dental practitioner to understand how those

different designs of implant-supported fixed prostheses influence the

biomechanical behaviors and develop better treatment plans to avoid

hazardous stress concentration in implant and its supporting bone. It

can prevent the biomechanical implant failure and enhance the

longevity of implants and prostheses.22

Three-dimensional finite element analysis (FEA) study is an

effective tool to investigate the results of biomechanical tests.23 It has

been employed to evaluate the biomechanical behavior such as stress

distribution pattern in the implant system and the bones in terms of

the implant-supported fixed prosthesis designs.24

3

A number of FEA studies have been conducted and compared the

stress distribution of different implant-supported fixed prostheses

designs.7,15,20,23 Khaki et al7 compared the stress distribution of

three-unit implant-supported fixed prostheses with splinted or

non-splinted restoration and the result showed that lower stress

values were induced in splinted implants. In contrast, Chen et al20

concluded in their study that when three mandibular posterior teeth

are missing, one implant for each missing teeth with separated

restoration was recommended. Batista et al15 evaluated the stress and

strain distributions of three-unit implant-retained prostheses with

pontic and cantilever designs. In accord with Chen’s result, they

suggested that placement of one implant for each missing tooth

provided lower stress and strain values and the use of cantilever

should be avoided when one implant for each missing tooth is not

possible because it could increase the chances of treatment failure

due to unfavorable biomechanical behavior.

Although there are several studies investigating the biomechanical

behaviors of different implant-supported fixed prostheses designs as

mentioned above, the influence of the designs to rehabilitate the

patients with multiple missing teeth especially in posterior quadrant

have still not been fully understood. Moreover, few studies were

conducted to compare the different designs simulating various clinical

scenarios including splinted or non-splinted restoration, pontic and

cantilever together as feasible treatment options.

Therefore, the aim of this study was to evaluate the effects of

various implant-supported fixed prosthesis designs with different

number of implants on mandibular posterior region verifying stress

distribution and displacement in components of implants and the bone

tissue by 3D finite element analysis.

4

Ⅱ. Material and methods

Total four three-dimensional finite element models of 4-unit

implant-supported fixed prostheses were developed based on a

patient’s computed tomography (CT) data to evaluate the stress

distributions around the bone and implants in partially and posteriorly

edentulous mandible. The models included implant-supported

prostheses with non-splinted (NS) and splinted (SP) prostheses,

pontic (PT) and cantilever (CT). An oblique load of 300 N on the

occlusal surface of the crowns with preload of 825 N in the abutment

screws was applied. The maximum Von Mises stress and maximum

displacement values of bone, teeth, implant system and crowns in the

models were analyzed to compare the biomechanical behaviors of the

models with different implant-supported prostheses designs. This

study was approved by the institutional review board of Seoul

National University Dental Hospital.

The partially edentulous mandible with missing teeth from first

premolar to second molar were created from the segmented CT scan

data using an image processing program (Mimics, Materialise). The

bone consisted of cancellous bone surrounded by approximately 2

mm-thick cortical bone. The geometries of external hex implant

system (Osstem US system; Osstem Implant Co.) was obtained from

the manufacturer. The dimensions of implant used in the study was 4

mm in diameter and 10 mm in height. Tetrahedral meshes of implant

systems and prostheses including remaining teeth and roots

surrounded by 0.3 mm-thick periodontal ligament in the mandible

were generated and assembled for finite element analysis with

meshing program (Visual-Mesh, ESI group).

Four finite element models with multiple 4-unit implant-supported

prostheses designs were created and each model was composed of

the mandible and teeth with implant, abutment, implant screw and

5

crown. Two models had 1 implant for each missing tooth with single

(NS) and splinted (SP) crowns. The model PT consisted of 3

implants on the first, second premolar and the second molar with

pontic. The model CT was comprised of 2 implants on the first

premolar and the first molar with distal cantilever (Fig. 1).

Configurations of the models are summarized in the Table 1.

The material properties of all components used for finite element

analysis were based on previous studies25,26 and summarized in the

Table 2. They were considered to be isotropic, homogeneous and

linearly elastic.27

Contact analysis was performed between the interfaces of implant

system among implant, abutment and screw with frictional coefficient

of 0.3.28,29 The implant was set to be tied to the abutment screw and

825 N of preload was applied on the abutment screw.30 The implant

was assumed to be bonded to the bone completely to simulate ideal

osseointegration. Total 300 N of oblique loading (50 N on premolars

and 100 N on molars respectively as applied 50 N in each buccal

cusp tip)15 at an angle of 11.3 degrees to the axis of the implant was

applied and the load was distributed to the buccal and occlusal

surface of the crown (Fig. 2).31,32

Finite element analysis was processed by Visual-Crash software

(Visual-Crash for PAM, ESI group). The maximum von Mises stress

and the displacement of each component of four different

implant-supported fixed prostheses models were compared and

evaluated.

Ⅲ. Results

Under oblique loading, stress concentration was observed in different

components of the models. Generally, higher stress appeared at the

abutment and the screw in all models representing similar stress

6

distribution patterns among the all models (Fig. 3).

As the number of the implants decreased, it had tendency to show

unfavorable results in implant, mainly for the cantilever configuration

(model CT). The maximum von Mises stress values in implant

increased from 577.7 MPa (model NS) to 616.8 (model SP), 649.3

(model PT) and 791.6 MPa (model CT). Model CT presented the

highest stress value (861.8 MPa) in abutment. The stress values of

Model PT were higher than those of Model NS or SP overall in

cancellous bone, fixture and crown. There was no significant

difference in stress values among the models in abutment and screw.

However, other results in different components such as bone and

crown other than implant were regardless of the reduction of number

of implants. Model CT presented the lowest stress values in cortical

bone and crown (112.2 and 220 MPa) among all models while model

PT showed the highest values in cancellous bone and crown (43.7

MPa and 305.4 MPa respectively). Furthermore, the maximum stress

values of model PT were mostly higher than those of model CT

except for implant despite of more number of implants. When

comparing single restoration with splinted crown, model NS had

lower stress values than model SP in cortical bone and fixture. In

cancellous bone and crown, model SP exhibited less stress than

model NS. The stress values in abutment and screw were not much

different between the model NS and SP (Table 3).

The maximum displacement occurred in abutment screws for all

models (Fig. 4). The displacement values of model NS were lower

than those of SP following the result of the maximum von Mises

stress values. Model PT presented higher displacement in abutment

and screw than model NS or SP. In addition, the displacements of

model PT in most components were higher than those of model CT.

Model CT showed the lowest displacement in cortical bone, fixture

and abutment (Table 4).

7

Ⅳ. Discussion

Four different designs were investigated for partially edentulous

mandible with missing teeth from first premolar to second molar in

this study. It was shown that a decrease in number of the implants

resulted in an increase of stress in the implants showing unfavorable

biomechanical behavior in the model as demonstrated in previous

studies.15,20,22 Yet, this trend was only limited to certain components in

the present study. The analyzed structure with 4 implants (model NS

and model SP) mostly had better biomechanical behavior than the one

with 3 implants with pontic configuration (model PT) following the

trend except for cortical bone. On the other hand, model CT with 2

implants presented the lowest stress value among all models in

cortical bone and crown and had lower stress concentration than that

of model PT in spite of less number of implants as an opposite result

to the previous studies.11,13,14 According to the results in this study, it

seemed that the use of pontic or cantilever with less number of

implants could be one of the alternative treatment options when

placing 1 implant for each missing tooth is impossible due to

limitations such as bone resorption, lack of space or financial reasons.

In this study, the applied force was total 300 N obliquely on the

prostheses. It was determined by the previous study15 to simulate the

human occlusal force which has numerous variations among the

individuals according to the anatomy of jaw and teeth or the textures

of food.33 Most of FEA studies to evaluate the biomechanical

behaviors of implant-supported prostheses applied the force only on

the certain point of the prostheses.15,22 Unlike those studies, the total

oblique force in this study was set to be distributed throughout the

area of buccal cusps and occlusal area of the crowns from the first

premolar to the second molar rather than concentrating the force on

particular portion of the prostheses. It may have influenced the

8

results of the study and can be distinguished from the other previous

studies.

A significant difference in stress value among all four models was

not found in abutment and screw. There existed similar stress

distribution and displacement patterns in all models with higher stress

and displacement values in abutment and screw compared to other

components. This may be due to the preload applied to the implant

system in this study. As the abutment screw is tightened, the

clamping force from the screw's head to the threads is generated to

hold the implant and the abutment together.34 The preload should be

more than occlusal force for achieving stability of the screw. The

preload of 825 N was used as an optimum preload in this study

which was reported to be ideally 75% of the yield strength of

screw.30 The fact that higher stress concentration and displacement

was detected mainly in screw can lead to the clinical complications

such as screw loosening or screw fracture. It would require to

consider retightening or replacing of screw later with care. Thus, it

can be said that taking preload condition into consideration for the

study would be inevitable to simulate the biomechanical behaviors of

implant-supported prostheses.

In most studies regarding splinting the implant crowns, they

suggested that splinting the crown together caused favorable stress

distribution to implant and the bone and had biomechanical

advantages.7,17,18 Khaki et al7 carried out the FEA study with three

implants in mandible from first premolar to first molar and found that

stress values of 3 seperated restorations were higher than 3

connected ones. Bergkvist et al17 demonstrated that stress values of 6

splinted implants were greatly lower than non-splinted implants in

maxilla. Guichet et al18 exhibited similar results and also found that

non-splinted restoration with heavier interproximal contacts showed

9

higher stress values than that with open contacts. They are not

consistent with the results of this study. Separated crowns have

shown the lower stress values than splinted ones in cortical bone and

implant in the study. In addition, little difference in stress was found

in abutment and screw between two models. Vigolo et al21 conducted

a 5-year prospective clinical study to compare the changes in

marginal bone level of splinted and non-splinted implants in maxilla

and concluded that marginal bone loss observed in non-splinted

implant was not statistically different to that in splinted one. Chen et

al20 also reported that there was no significant difference between

single and splinted crowns for three implants supported fixed

prostheses in posterior mandible. They mentioned that it should be

evaluated depending on different areas of dental arch, number of

implants, span and occlusal scheme to decide which one is more

beneficial.20 In addition, non-splinted crown could be better for

maintaining oral hygiene allowing better access to interproximal

surfaces.35

A long-term success of dental implant with implant-supported fixed

prostheses requires several considerations with good control of

biomechanical factors.20 To evaluate the performance of

implant-supported prostheses with various configurations, FEA may

be a useful tool as computer-aided analyses. It has been widely used

to predict stress distributions at implant and prostheses including

peri-implant regions and assess the influences of implant and

prostheses designs in different clinical situations.22 However, it needs

to be pointed out that several assumptions which the materials used

are isotropic, homogeneous and linearly elastic27 were included for this

study to simplify the study.

For further study, it would be necessary to develop the analyzed

FEA models of the study by adding more critical situations with a

10

variety of implant length, implant design and other prosthetic

configurations.

Ⅴ. Conclusion

Within the limitation, the following conclusions can be drawn from

this 3D finite element analysis.

1. The reduction of number of implants provided lower stress

concentration in certain components of implant-supported fixed

prostheses, especially in implant. However, the results on stress

concentration in other components such as bone or crowns were

regardless of the number of implants or different prosthetic

designs.

2. When placing one implant for each missing tooth is not possible

due to critical clinical situations, the use of pontic or catilever

could be also one of alternatives as treatment options for partially

edentulous patients.

11

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16

ModelNumber of

ImplantsRehabilitation

Number of

elements

Number of

nodes

NS 4 Non-splinted 1053884 205890

SP 4 Splinted 1079456 210057

PT 3 Pontic 845361 165557

CT 2 Cantilever 652196 127181

TABLES

Table 1. Description of models.

17

Component Elastic modulus (GPa) Poisson ratio

Cortical bone 13.7 0.3

Cancellous bone 1.37 0.3

Tooth dentin 41 0.3

Periodontal ligament 3x10-5 0.45

Titanium alloy 102 0.3

Gold alloy 100 0.3

Table 2. Material Properties used in the study.25,26

18

Model NS SP PT CT

Cortical bone 151.0 182.3 146.9 112.2

Cancellous bone 36.8 31.9 43.7 33.1

Implant 577.7 616.8 649.3 791.6

Abutment 860.9 861.0 860.9 861.8

Screw 862.3 862.4 862.3 862.0

Crown 298.4 297.7 305.4 220.0

Table 3. The maximum von Mises stress vales (MPa) in each

component of the models.

19

Model NS SP PT CT

Cortical bone 57.7 69.6 68.6 56.6

Cancellous bone 43.3 45.7 48.3 46.6

Implant 47.7 39.2 43.6 35.0

Abutment 71.8 71.8 77.4 67.8

Screw 81.5 128.8 135.2 125.1

Crown 65.2 71.4 68.7 95.7

Table 4. The maximum displacement vales (㎛) in each component of

the models.

20

FIGURES

Fig. 1. Finite element models. A, four implants with non-splinted

crowns (NS); B, four implants with splinted crowns (SP); C, three

implants with pontic (PT); and D, two implants with cantilever (CT).

A B

C D

21

Fig. 2. The applied force of finite element models. A, Mesial view,

oblique loading at angle of θ=11.3 degrees from implant axis B,

Occlusal view, illustrating the location of the applied force of total

300 N (50 N on premolars and 100 N on molars respectively, load

was distributed to the buccal and occlusal surfaces of the crowns)

A B

22

Fig. 3. Overall stress concentrations of the models in MPa. A, model

NS; B, model SP; C, model PT and D, model CT

A B

C D

23

Fig. 4. Maximum displacement of the models in ㎛. A, model NS; B,

model SP; C, model PT and D, model CT

A B

C D

24

국문초록

하악 구치부에서 임플란트 개수와 다양한

보철디자인이 임플란트-지지고정성보철물의

생역학적 거동에 미치는 영향:

삼차원 유한요소연구

서울대학교 대학원 치의과학과 치과보철학전공

(지도교수 권 호 범)

정 원 경

1. 목 적

이 연구의 목적은 하악 구치부 부분 무치악 모형에서 다양한 디자인과

임플란트 개수를 가진 임플란트-지지 고정성 보철물을 생역학적으로 분

석 하는 것이다.

2. 방 법

하악 구치부 부분 무치악인 하악골, 잔존치아, 임플란트 시스템 그리고

상부 보철물로 이루어진 유한요소 모형을 유한요소 제작 프로그램

(Visual-Mesh, ESI group)을 이용하여 제작하였다. 하악골과 치아는 환

자의 CT 데이터를 기반으로 제작되었으며 임플란트 시스템은 제조회사

로부터 제공되었다 (Osstem US system; Osstem Implant Co.). 각기 다

른 임플란트 개수와 디자인을 가진 네 개의 모형은 다음과 같다: 제1소

구치부터 제2대구치까지 하악 구치부 네개의 상실치아에 모두 임플란트

를 식립하여, 총 네 개의 임플란트와 함께 연결 고정 되지 않은 단일 보

철물 (NS); 네 개의 임플란트와 서로 연결 고정 되어있는 보철물 (SP);

제1소구치, 제2소구치 그리고 제2대구치에 총 세 개의 임플란트와 가공

치(pontic)를 포함한 보철물 (PT); 제1소구치와 제1대구치에 총 두 개의

임플란트와 캔틸레버를 포함한 보철물 (CT). 골- 임플란트의 계면은 고

정 된 것으로 설정하였고, 임플란트와 임플란트 시스템의 구조물 사이의

계면에는 마찰계수 0.3의 경계조건을 설정하였다. 임플란트 나사에 825N

의 전하중을 가한 후, 11.3˚의 각도로 총 300 N 경사하중을 보철물의 교

합면에 가하였다. 그리고 관찰 된 각각의 구조물들의 최대등가응력

(Max. von Mises stress)의 분포와 변위를 비교분석 하였다.

3. 결 과

임플란트에서는 임플란트의 식립 개수가 적은 모델일수록 응력이 증가하

는 것을 보여주었으며 캔틸레버 모델에서의 응력 값이 가장 높았다. 반

면에 골이나 금관과 같은 구조물에서는 오히려 캔틸레버 모델이 각각

112.2 와 220 MPa로 다른 모델들보다 더 적은 응력 값을 보여주었다.

피질골과 임플란트에서는 연결 고정되지 않은 단일 보철물의 응력이 각

각 151 과 577.7 MPa로, 182.3 과 616.8 MPa인 연결 고정 된 모델보다

적은 응력 값을 나타내었으나 해면골과 금관에서는 반대로 연결 고정 된

보철물이 31.9 와 297.7 MPa 로, 36.8 과 298.4 MPa인 단일 보철물보다

더 적은 응력 값을 보여주었다.

4. 결 론

임플란트-지지 고정성 보철물의 몇몇 구조물들은 임플란트 개수의 감소

에 따른 더 큰 응력 분포를 의 패턴을 보여주긴 하였지만 골이나 금관과

같은 다른 구조물에서는 임플란트의 개수와 응력 분포 사이에 유의미한

관련성이 보이지 않았다. 따라서 임상에서 각각의 결손 치아에 하나의

임플란트 식립이 어려울 경우에는 가공치(pontic)나 캔틸레버를 포함한

디자인의 보철물 또한 유용한 치료 옵션이 될 수 있다.

………………………………………………………………………………………

주요어 : 임플란트-지지 고정성 보철물, 생역학적 분석, 응력분포,

유한요소법

학 번 : 2016-22041